Did the horse and carriage market account for an equivalent percentage of the economy as the auto market does noe?

Definitely not my field, but this might be at least somewhat helpful. I can't answer for the economy as a whole (and you'll need to be specific about which country and time period you're most interested in anyway!), but I might be able to give a rough field of reference.

In Laura Ingalls Wilder's journals and series of accounts written of late nineteenth century America, commentary on horses appears very frequently. Little House on the Prairie is the book the most people have heard of, but Wilder was a prolific writer who left journals, letters, and an entire series on her child and young adulthood. Horse health, temperament, speed, and stamina are referenced constantly by Wilder and the people who appear in her work. It definitely sticks out to modern readers, but to them, it was just background commentary on an ever-present part of their lives. Horse health and ability played a huge role in a family's fortunes, and a sick, injured, or (much worse) stolen horse could economically cripple someone. As with the cars of today, they were significant investments, and people were just as edgy and anxious about their horses then as they tend to be about their cars today.

The book Farmer Boy is an account of her husband's childhood in the upstate New York of the late 1860s, and probably contains the most direct references to your question. Almanzo's father sells a pair of four year old Morgan horses for $200 each, which was considered an excellent price. Quality horses were more routinely sold for roughly $175, but Mr. Wilder markets them to the horse buyer like this:

Father led out the colts. They were perfectly matched Morgans, exactly the same size, the same shape, the same bright brown all over, with the same white stars on their foreheads. They arched their necks and picked up their little feet daintily.

"Four years old in May, sound in wind and limb, not a blemish on them," Father said. "Broken to drive double or single. They're high-spirited, full of ginger, and gentle as kittens. A lady can drive them."

NB: That particular bit is important. Horses that constantly pulled at the reins and didn't want to take direction from the driver were difficult to control at best and dangerous at worst. Due to size and strength issues, women generally had more problems controlling a stubborn team than a man did, so a horse that wouldn't be a hassle for any driver was worth a lot more than one that wasn't.

... The buyer felt the colts' legs, he opened their mouths and looked at their teeth. Father had nothing to fear from that; he had told the truth about the colts' age. Then the buyer stood back and watched, while Father took each colt on a long rope and made it walk, trot, and gallop in a circle around him.

"Look at that action," Father said.

Not long after this point in the narrative, they go on a test drive, which just cements how much the whole process feels like buying a car in this day and age.

One note I should probably include is that the Morgan horse of the American 19th century was particularly popular for its versatility -- you could use them for driving, pleasure riding, or hitch them for farm work -- but more specialized breeds were often developed for greater efficiency in specific fields. Almanzo's father later considers and then rejects the possibility of buying what he refers to as a Belgian draft horse, though if Laura's account is accurate, they are far more likely to have been Percherons (another heavy draft that was first seeing export to the United States). He shrugs them off under the rationale that the feed costs for such a heavy breed would not outweigh the benefit of potentially better or faster plowing, and they were not as fast as Morgans for driving. So that, too, is not entirely unlike the car market of the 21st century and the oft-repeated advice not to buy more car then you need.

Anyway, the end result was that, despite the horse buyer's reluctance, Mr. Wilder did wind up selling the horses for $200 each. I only have access to a rough inflation calculator, so this will be highly imperfect, but $200 in 1867 would be worth roughly $3,200 in 2014 dollars. Again, that was considered a high price in the upstate New York of 1867; I don't know how universal that would be for the rest of New York, much less the U.S. or the rest of the world.

So figure $6,400 for the full team in today's dollars, and that brings us to the question of what a carriage would cost. Unfortunately, here I have much less information.

Carriages were not uniform things; as with horses, there was a wide range of type and quality, and a corresponding range in cost. Every farmer needed a wagon and/or cart, but carriages existed for no other reason than transport/driving. Laura's family was fairly poor while she was growing up and did not own anything other than a wagon. Not surprisingly, carriage vehicles tend to pop up in her accounts as status symbols, and in her young adult life, buggies and cutters (two-passenger sleighs) on the Dakota prairie are great marks of prestige.

However, I'm very reluctant to say much beyond that, because Laura was a farmer for most of her life and had little experience with the wide variety of carriage types in major cities in the States, much less elsewhere. The type of horses bred specifically for coach work -- the Cleveland Bay, the now-extinct Yorkshire coach horse, the Hanoverian, etc. -- do not appear in her writings at all. In fairness, I believe these breeds were also more popular in Europe than the U.S. at the time, but it's telling that all of the horses in her works are Morgans, drafts, or mustangs. Carriage horses certainly existed in the U.S. and Canada at the time -- the work I'll link below references very high-quality imported American and Canadian carriage horses on the London market of the 1890s -- but Laura wasn't in a position to see much of them.

What little I do know (largely from commentary in annotated versions of 19th century literature) is that four-wheeled carriage vehicles were typically heavier and more expensive than two-wheeled variants like the gig, and there was a very wide variety of designs that changed much as human fashions do. The "phaeton and ponies" referenced in Pride and Prejudice (published in 1813) went through substantially different designs between its introduction in the late 18th century and Queen Victoria's variant in the late 19th century.

Your question made me curious, and while nosing around a bit I found The Horse World of London, which was published in 1893 (you can find a digital copy here courtesy of the University of Michigan) and this might contain some useful information. This chapter on the carriage horse of London is particularly notable and does contain some notes on the expense involved with buying or hiring a team and carriage. However, I'm utterly lost with respect to "translating" that to 21st century dollars. However, you might find someone here who can.